In this last direction, for the classical Bessel function \(J_{\nu }(x)\) , since it fails to satisfy the properties of the trigonometric function, an analogue of the Riemann–Lebesgue theorem [1]} was proved, not for the Bessel function \(J_{\nu }(x)\)  itself but for the function
\( T_n(t,x)=\sum _{m=1}^{n}\frac{2J_{\nu }\left(j_m x\right)J_{\nu }(j_m t)}{J_{\nu +1}^2(j_m)} ,\) 
